here, read this
bettas have to should be fed a portion (tiny pinch of flakes or 2 pellets) twice daily. and they have to be kept at 77-79 degrees F. if its too cold they will get very inactive and prone to illnesses.
so you should get a thermometer and a heater. but a 1/2 gallon is too small for a heater so you'll probly have to get at least a 2 gallon tank with a 10 watt micro heater.
its always handy to get a master liquid test kit to test ammonia, nitrite, and nitrate, and usally ph. if you get a bigger tank also these parameters will be more stable which is good for you and the fish.